If f(x) = (3x-1)/(x^2 -2) find f ' (1)

f(x) = (3x-1)/(x^2 - 2)

Let
us differentiate f:

f(x) = u/v    such
that:

u= 3x-1   ==>   u' =
3

v= x^2 -2   ==>   v'=
2x

==> f'(x) = (u'v-
uv')/v^2

               = (3(x^2 - 2) - (3x-1)2x ]/(x^2
-2)^2

                = (3x^2 - 6 - 6x^2 + 2x)/(x^2 -
2)^2

                  = (-3x^2 + 2x - 6)/(x^2
-2)^2

Now let us substitute with x=
1

==> f'(1) = (-3 + 2 -
6)/(-1)^2

                 = -7/1 =
-7

==> f'(1) =
-7